[Fyron]

This post assumes the default Peaceful happiness type. Neutral is absolutely worthless and police troops have the same benefits with Bloodthirsty.

Note that the "police troops" I use are exactly your "security troops." They are always small, and weapons are optional. Some people like to arm them to get a ready source of troops to handle rebellion events and such, as well as extra defense against invasions. Not that they help much against a large transport filled with shielded large troops, of course.

You can get a max change of 20% (aka 200) up or down per turn. 100 troops is sufficient for getting this 200 (at 2 per troop). The 20 is just for a bit of redundancy. The purpose of police troops is not to make the people happy when all goes well. They are there to keep the people jubilant through the worst of situations. It is disturbingly easy for an unprotected empire to go from jubilance to riots in a short while if a war takes a turn for the worst. The troops can prevent this from happening and provide you with the possibility for recovery.

With 120 troops, you can suffer up to 240 happiness points worth of losses per turn and not have any decrease in happiness. This equates to 240 ships or almost 5 planets in a single turn. You could lose 2 planets and 140 ships and suffer no ill affects to happiness throughout the empire. In most games, I find it highly unusual to be able to lose more than this in a single turn. If you do, you have probably already lost and are just being mopped up by the enemy. But even if you lose more than this in one turn, chances are you won't lose just as much in the next turn, so having enough troops to get 240 percent increase in happiness will bring you right back up to jubilance, with an added window of still being able to lose 1 planet or 40 ships and not matter.

Granted, against the AI, this isn't always necessary, as the AI is not too challenging. It mostly applies to multiplayer games.

No amount of ships can achieve these same riot protection results. Having 20 ships stationed over every planet or 67 in every system (to get 200 happiness increase per turn) is generally a very bad idea, as your offensive forces will be few and far between (or even nonexistent).